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For the circuit shown find Av, Ri and Ro.

Mumbai University > Electronics Engineering > Sem 4 > Discrete Electronic Circuits

Marks: 10M

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enter image description here

Given:

rd=40kΩ

kn=0.4×103

VGS(th)=3V

Av=gm(rd||RD)

Rin=R1||R2

Ro=rd||RD

We know that,

gm=2kn(VGSQVT)

gm=2×0.4×103(VGSQ3)……………..(1)

To find gmandVGSQ we have to perform DC analysis, all the coupling capacitor acts as open circuit, as shown in Figure 2:

enter image description here

IDS=kn(VGSVT)2

IDS=0.4×103(VGS3)2----------------(2)

But voltage divider biasing equation is,

VR2VGS(IDS×RS)=0

VGS=VR2(IDS×1.2KΩ)----------------(3)

Using Voltage divider rule,

VR2=VGS=VDD×R2R1+R2

=30×10MΩ10MΩ+40MΩ

=6V

Substitute in equation (3),

VGS=6(IDS×1.2KΩ)------------------(4)

Put equation (4) in (2),

IDS=0.4×103(6(IDS×1.2KΩ)3)2

IDS=0.4×103(3IDS×1.2KΩ)2

Solving above equation we get two values of IDS,

IDS=5.625mAorIDS=1.11mA

IDS=5.625mA IDS=1.11mA
VGS=6(IDS×1.2KΩ)=6(5.625mA×1.2KΩ)=0.75V VGS=6(IDS×1.2KΩ)=6(1.11mA×1.2KΩ)=4.668V
0.75V<VT 4.668V>VT

Hence from above observation, select IDSQ=1.11mAbecauseVGS>VT

Substitute in equation (4),

VGSQ=4.668V

Hence substitute VGSQ in equation (1),

gm=2×0.4×103(4.6683)

gm=1.3344×103

Av=gm(rd||RD)

Av=1.3344×103(40kΩ||3.3KΩ)

Av=-4.06

Rin=R1||R2

Rin=40MΩ||10MΩ

Rin=8MΩ

Ro=rd||RD

Ro=40MΩ||3.3KΩ

Ro=3.048KΩ

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